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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 9 · 40 questions
TalentJR

How to solve it (180 is the magic number): The three angles of a triangle add up to 180°. An exterior angle equals the sum of the two interior angles opposite it. An isosceles triangle has two equal angles, opposite its two equal sides. Angles on a straight line add up to 180°; vertically opposite angles are equal.

NameDateTime takenScore ___ / 40
  1. 1.Two angles of a triangle are 20° and 125°. What is the exterior angle at the third corner? (a) 35° (b) 55° (c) 145° (d) 160°
  2. 2.Two angles of a triangle are 65° and 80°. What is the third angle? (a) 100° (b) 35° (c) 115° (d) 145°
  3. 3.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 80° (b) 20° (c) 10° (d) 100°
  4. 4.Two straight lines cross. Two vertically opposite angles add up to 40°. What is each of the other two angles? (a) 140° (b) 20° (c) 160° (d) 320°
  5. 5.Two angles of a triangle are 25° and 80°. What is the exterior angle at the third corner? (a) 105° (b) 100° (c) 155° (d) 75°
  6. 6.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 30° (b) 150° (c) 60° (d) 75°
  7. 7.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 25° (b) 65° (c) 115° (d) 50°
  8. 8.Two angles of a triangle are 75° and 25°. What is the third angle? (a) 100° (b) 105° (c) 155° (d) 80°
  9. 9.Two angles of a triangle are 35° and 110°. What is the third angle? (a) 145° (b) 70° (c) 215° (d) 35°
  10. 10.Two straight lines cross. One of the angles is 125°. What is the angle next to it on the same straight line? (a) 235° (b) 125° (c) 56° (d) 55°
  11. 11.Two angles of a triangle are 70° and 50°. What is the exterior angle at the third corner? (a) 130° (b) 60° (c) 120° (d) 110°
  12. 12.Two angles of a triangle are 45° and 70°. What is the third angle? (a) 110° (b) 65° (c) 115° (d) 135°
  13. 13.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 130° (b) 40° (c) 80° (d) 50°
  14. 14.Two angles of a triangle are 25° and 50°. What is the third angle? (a) 155° (b) 130° (c) 105° (d) 75°
  15. 15.Two angles of a triangle are 75° and 90°. What is the third angle? (a) 15° (b) 90° (c) 105° (d) 165°
  16. 16.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 125° (b) 35° (c) 55° (d) 70°
  17. 17.Two straight lines cross. Two vertically opposite angles add up to 280°. What is each of the other two angles? (a) 140° (b) 41° (c) 40° (d) 80°
  18. 18.Two angles of a triangle are 30° and 45°. What is the exterior angle at the third corner? (a) 75° (b) 135° (c) 150° (d) 105°
  19. 19.Two angles of a triangle are 20° and 115°. What is the third angle? (a) 135° (b) 45° (c) 65° (d) 160°
  20. 20.Two straight lines cross. Two vertically opposite angles add up to 340°. What is each of the other two angles? (a) 20° (b) 10° (c) 170° (d) 11°
  21. 21.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 70° (b) 60° (c) 30° (d) 120°
  22. 22.Two angles of a triangle are 60° and 60°. What is the third angle? (a) 120° (b) 60° (c) 61° (d) 240°
  23. 23.Two angles of a triangle are 50° and 30°. What is the exterior angle at the third corner? (a) 100° (b) 130° (c) 150° (d) 80°
  24. 24.Two angles of a triangle are 60° and 110°. What is the third angle? (a) 170° (b) 10° (c) 70° (d) 120°
  25. 25.Two angles of a triangle are 40° and 105°. What is the exterior angle at the third corner? (a) 75° (b) 145° (c) 140° (d) 35°
  26. 26.Two straight lines cross. One of the angles is 70°. What is the angle next to it on the same straight line? (a) 290° (b) 110° (c) 20° (d) 70°
  27. 27.Two angles of a triangle are 75° and 40°. What is the third angle? (a) 115° (b) 105° (c) 140° (d) 65°
  28. 28.Two straight lines cross. One of the angles is 40°. What is the angle next to it on the same straight line? (a) 320° (b) 40° (c) 50° (d) 140°
  29. 29.Two angles of a triangle are 80° and 60°. What is the third angle? (a) 120° (b) 100° (c) 40° (d) 140°
  30. 30.Two angles of a triangle are 20° and 95°. What is the exterior angle at the third corner? (a) 160° (b) 85° (c) 65° (d) 115°
  31. 31.Two angles of a triangle are 30° and 55°. What is the exterior angle at the third corner? (a) 95° (b) 125° (c) 85° (d) 150°
  32. 32.Two angles of a triangle are 50° and 25°. What is the exterior angle at the third corner? (a) 75° (b) 105° (c) 155° (d) 130°
  33. 33.Two angles of a triangle are 40° and 20°. What is the exterior angle at the third corner? (a) 140° (b) 120° (c) 60° (d) 160°
  34. 34.Two angles of a triangle are 70° and 90°. What is the third angle? (a) 160° (b) 90° (c) 110° (d) 20°
  35. 35.Two angles of a triangle are 20° and 60°. What is the third angle? (a) 80° (b) 160° (c) 100° (d) 120°
  36. 36.Two angles of a triangle are 40° and 90°. What is the exterior angle at the third corner? (a) 130° (b) 140° (c) 90° (d) 50°
  37. 37.Two angles of a triangle are 50° and 80°. What is the exterior angle at the third corner? (a) 130° (b) 100° (c) 50° (d) 230°
  38. 38.Two angles of a triangle are 35° and 40°. What is the exterior angle at the third corner? (a) 145° (b) 105° (c) 140° (d) 75°
  39. 39.Two straight lines cross. One of the angles is 50°. What is the angle next to it on the same straight line? (a) 310° (b) 40° (c) 130° (d) 50°
  40. 40.Two angles of a triangle are 50° and 90°. What is the exterior angle at the third corner? (a) 130° (b) 140° (c) 90° (d) 40°

Answer key

  1. 145°
  2. 35°
  3. 20°
  4. 160°
  5. 105°
  6. 75°
  7. 50°
  8. 80°
  9. 35°
  10. 55°
  11. 120°
  12. 65°
  13. 80°
  14. 105°
  15. 15°
  16. 70°
  17. 40°
  18. 75°
  19. 45°
  20. 10°
  21. 60°
  22. 60°
  23. 80°
  24. 10°
  25. 145°
  26. 110°
  27. 65°
  28. 140°
  29. 40°
  30. 115°
  31. 85°
  32. 75°
  33. 60°
  34. 20°
  35. 100°
  36. 130°
  37. 130°
  38. 75°
  39. 130°
  40. 140°

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